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Scale 1695: "Phrodyllic"

Scale 1695: Phrodyllic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Phrodyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,7,9,10}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3885
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}441.82
D♯{3,7,10}342
A{9,1,4}342
Minor Triadscm{0,3,7}341.91
gm{7,10,2}242.27
am{9,0,4}341.91
Diminished Triadsc♯°{1,4,7}242.09
{4,7,10}242.09
{7,10,1}242.36
{9,0,3}242.18
a♯°{10,1,4}242.27
Parsimonious Voice Leading Between Common Triads of Scale 1695. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A D#->e° gm gm D#->gm g°->gm a#° a#° g°->a#° a°->am am->A A->a#°

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Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1695 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2895
Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
3rd mode:
Scale 3495
Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
4th mode:
Scale 3795
Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
5th mode:
Scale 3945
Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
6th mode:
Scale 1005
Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
7th mode:
Scale 1275
Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
8th mode:
Scale 2685
Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [1695, 2895, 3495, 3795, 3945, 1005, 1275, 2685] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1695 is 3885

Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1695 is chiral, and its enantiomorph is scale 3885

Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic

Transformations:

T0 1695  T0I 3885
T1 3390  T1I 3675
T2 2685  T2I 3255
T3 1275  T3I 2415
T4 2550  T4I 735
T5 1005  T5I 1470
T6 2010  T6I 2940
T7 4020  T7I 1785
T8 3945  T8I 3570
T9 3795  T9I 3045
T10 3495  T10I 1995
T11 2895  T11I 3990

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1567Scale 1567, Ian Ring Music Theory
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 1183Scale 1183: Sadian, Ian Ring Music TheorySadian
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.